Real Space Renormalization Group for One-Dimensional Ising Chains

TL;DR

This paper applies real space renormalization group techniques to analyze various one-dimensional Ising chains, including ordered, alternate, and Fibonacci chains, providing an accessible pedagogical approach.

Contribution

It extends existing RNG methods to non-trivial 1D Ising chains like the alternate and Fibonacci models, broadening their applicability.

Findings

Successfully applied RNG to new Ising chain variants

Provided a pedagogical framework suitable for undergraduates

Extended the decimation approach to complex 1D models

Abstract

We apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to certain non-trivial situation namely, the Alternate Ising Chain and Fibonacci Ising chain. Our approach is pedagogical and accessible to undergraduate students who have had a first course in statistical mechanics.